Article

Fast inversion of Chebyshev-Vandermonde systems

Numerische Mathematik (Impact Factor: 1.61). 08/1995; 67(1). DOI: 10.1007/s002110050018
Source: CiteSeer

ABSTRACT

This paper contains two fast algorithms for
inversion of
Chebyshev--Vandermonde
matrices of the first and second kind. They are
based on special representations of the Bezoutians of Chebyshev polynomials of
both kinds. The paper also contains the results of numerical
experiments which show that the algorithms proposed here are not only much
faster, but also more stable than other algorithms available. It is also
efficient to use the above two algorithms for solving Chebyshev--Vandermode
systems of equations with preprocessing.

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    • ", Tr [28], GO [16] P [25], Tr[28] BP[9] Chebychev-V Chebychev poly GO [14] GO [14] RO[26] Three-Term-V Real orthogonal poly Vs [29], GO [14] CR [10] Hi[27] Szegö–V Szegö polynomial O [23] O [24] BEGKO [1] Quasiseparable Quasiseparable BEGOT [4] BEGOT [6], BEGKO [2] Vandermonde polynomial BEGOT [5] BEGOTZ [7] Table 1: Fast O(n 2 ) inversion for polynomial–Vandermonde matrices. Inversion formulas and fast system solving are classical applications in Displacement Theory. "
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